I think the most common conflict boils down to external pressure versus internal truth. You'll see families arranging marriages for business or status, pushing the couple into proximity while ignoring their actual feelings. That creates so many quiet, simmering scenes where characters are forced to spend time together under everyone's watchful eyes.
What I find more interesting than the obvious pushback, though, is the guilt. A character might start to develop real feelings but then wrestle with the idea that those feelings are illegitimate because they originated from coercion. It's a fantastic way to explore autonomy and self-doubt. The resolution often hinges on dismantling the external pressure so the relationship can be re-evaluated on its own terms, free from obligation.